On the effective permeability of a heterogeneous porous medium: the role of the geometric mean

This paper uses experimental data derived from surface permeability tests conducted on a bench-scale 508?mm cuboidal sample of Indiana Limestone. These results are used in combination with computational modelling to test the hypothesis that the geometric mean is a good proxy to represent permeability when the spatial distribution of the permeability for the heterogeneous rock, with no evidence of hydraulic anisotropy or fractures, is log-normal. The predictive capabilities of the geometric mean as a measure of the effective permeability are further assessed by examining specific examples where three-dimensional flows are initiated in the heterogeneous domain and where the equivalent homogeneous problem gives rise to purely circular flows that have exact solutions. The approach is also applied to examine a hypothetical hydraulic pulse test that is conducted on a cuboidal region with sealed lateral boundaries, consisting of the experimentally measured heterogeneous distribution of permeability and an equivalent homogeneous region where the permeability corresponds to the geometric mean.